# Sampling Techniques (ISS (Statistical Services) Statistics Paper III): Questions 12 - 17 of 30

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## Question number: 12

» Sampling Techniques » Stratified Random Sampling

Appeared in Year: 2010

### Describe in Detail

Explain the concept of stratification in stratified simple Random sampling. What is proportional and optimum allocation in stratified simple Random sampling? With usual notations show that: V () _{opt } < V () _{prop} < V () _{ran}

### Explanation

**Stratification: **

Stratification means division into layers, classes or categories. Past or some other information related to the character under study may be used to divide the population into various groups. Then simple random sampling or systematic sampling is applied within each stratum.

The strata should be mutually exclusive and exhaustive:

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## Question number: 13

» Sampling Techniques » Cluster Sampling With SRS - Intra-Class Correlation Coefficient

Appeared in Year: 2010

### Describe in Detail

What is cluster sampling? In the case of cluster sampling for proportions, obtain an unbiased

Estimator of population proportion. Also, compute variance of your estimator.

### Explanation

**Cluster sampling: **

Cluster sampling is a type of sampling method. In this method, the population is divided into separate groups, called clusters. Then, a simple random sample of clusters is selected from the population. Then analysis is done on the data from the obtained sampled clusters.

The samplings lead to several difficulties if the popula

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## Question number: 14

» Sampling Techniques » Simple Random Sampling With and Without Replacement

Appeared in Year: 2011

### Write in Short

**Explain the concept of simple random/sampling with and without replacement. In a simple Random sampling, show that is an unbiased estimator of . **

## Question number: 15

» Sampling Techniques » Stratified Random Sampling

Appeared in Year: 2011

### Describe in Detail

Let for a stratified random samplingwhereis constant, is the-cost per unit-in i^{th }stratum**, ** is the mean square based on** **units.

Estimate the sample sizen under optimum allocation for fixed cost**. **

### Explanation

Under optimum allocation, are obtained such that

(i) minimize the variance of the estimate for (a) fixed sample size n;

(i) var (is minimum for fixed n

(ii) var (is minimum for fixed total cost C

(iii) Total cost C is minimum for fixed value of var (

And the cost function C in stratified sampling is given by the linea

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## Question number: 16

» Sampling Techniques » Simple Random Sampling and Systematic Sampling

Appeared in Year: 2011

### Describe in Detail

Explain aligned sample and unaligned systematic sampling method

### Explanation

Systematic sampling in two dimensions:

The linear systematic sampling can be extended for two dimensions populations. here it is assumed that the n m k l population units are arranged in the form of ml rows, each containing nk units and a systematic sampling of m n units is selected. There are two procedures adopted to draw a sample of size mn.

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## Question number: 17

» Sampling Techniques » Simple Random Sampling and Systematic Sampling

Appeared in Year: 2010

### Describe in Detail

Explain the concepts of linear and circular systematic sampling giving suitable illustrations.

Further, show that for linear systematic sampling, sample mean is an unbiased estimator for population mean.

### Explanation

Let us suppose that N sampling units are serially numbered from 1 to N in some order and a sample of size n is to be drawn in such a way that N is expressible as a product of two integers *n* and *k. *

N = nk → k = Where k, usually called the sampling interval. k is taken as the integer nearest to

**Linear systematic sampling: **

To draw a sample of

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